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Challenge

A man walks into a room of 9 people. Heshakes everybodys hand.Then each of the guests shake everyones

hand.

How many handshakes are there intotal?

How do you know?

45

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Key Learning Points

By the end of this lesson you will:

- be able to expand two brackets to get

a quadratic expression

Quadratic Expressions

Key words: quadratic expression, expand, brackets, grid, FOIL

2 ( 2x + 3) 2 ( 2x - 3) 3 (x - 3) 4 ( 8 3x)

4x + 632 12x3x - 9 4x - 6

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Discussion

(x + 1) ( x + 1) = x2 + x + x + 1

(x + 1) (x 1) = x2 + x x 1

(x 1) (x + 1) = x2 x + x 1

(x 1) (x 1) = x2 x x + 1

Why?

3 minutes turn to the person next to you

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Success Criteria

Grade D: I can collect some like terms towrite expressions in their simplest form

Grade C: I can expand a single bracket and

write it in its simplest formGrade B: I can expand two brackets and

write them it in its simplest form

Grade A: I can expand two brackets wherethe x coefficients are not 1.

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Expanding two brackets

(x + 2) (x + 3)

Method 1 (GRID)

x + 2

x

+ 3

x2

+ 3x

+ 2x

+6

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Expanding two brackets

(x + 2) (x + 3)

Method 2 (FOIL)

First

Outer

Inner

Last

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Expanding two brackets

(x + 2) (x + 3)

Method 2 (FOIL)

FirstOuter

Inner

Last

x2 + 3x + 2x + 6

(x + 2) (x + 3)

Method 1 (GRID)

x + 2

x

+ 3

x2

+ 3x

+ 2x

+6

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Try it for yourself...

Page 82Exercise 5:4

Extension:(x + 2) (3x 1)2( x + 2) + 3(3x 1)

How are these two expressions similarand how do they differ?

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Reflection

What have I learnt?

What grade am Iworking at? How doI know?

What do I need to doto make progress?

Try these...

(x + 1) ( x + 2)

(2x + 1) (2x + 3)

(3x 1) (2x 4)